Hall devices are extensively used in many kinds of applications for high precision magnetic measurement. Horizontal Hall devices or “Hall plates” are sensitive to the magnetic field component orthogonal to the chip plane. In contrast, vertical Hall sensors are capable of measuring in-plane magnetic field components. Both types of Hall sensors typically have a residual offset, i.e. a residual voltage or signal measured when the sensor is placed in a zero magnetic field. Horizontal Hall sensors or Hall plates can be designed to have a 90° rotational symmetry, for example. In combination with a so-called spinning current scheme it is typically possible to significantly reduce the residual offset error, because it partially cancels out when adding or subtracting output signals of the horizontal Hall sensor measured during different clock phases of the spinning current scheme. According to the spinning current technique, the supply contacts and the sense contacts of the Hall sensor are periodically swapped or changed in a round-robin (cyclic) manner. Vertical Hall sensors, on the other hand, typically show a relatively large inherent offset error. The spinning current scheme can also be applied to vertical Hall sensors, but its offset-reducing effect typically is not as high as with horizontal Hall sensors. The reason is that most designs for vertical Hall sensors do not provide a, for example, 90° symmetry with respect to supply contacts and sense contacts of the vertical Hall sensor.
Moreover, vertical Hall sensors are also affected by the so called junction-field-effect (JFE) in analogy to the working principle of the junction-field-effect transistor (JFET). The junction-field-effect is caused by a voltage-dependent thickness of an isolating depletion layer formed by a reverse biased p-n junction that confines the active volume or Hall effect region of the Hall sensor. During operation of the vertical Hall sensor, the Hall voltage and the magnetoresistance effect lead to potential variations inside the device and the active volume is deformed causing some kind of JFET-nonlinearity.
Basically, four different sources of non-ideal behavior can be distinguished from the output signal point-of-view of a Hall device. The Hall voltage and the magnetoresistance effect are both causing JFET non-linearity. Two other effects are referred to as material non-linearity and geometry related non-linearity. These latter two effects are technology-independent and typically exist also in any infinitely thin conventional Hall plate.
According to the junction-field-effect, the p-n junction in a buried semiconductor (e.g. silicon) Hall device between the shield (surrounding substrate) and active zone creates a voltage dependent depletion layer. The thickness of the depletion layer is not uniform, but varies locally and depends upon the local potential of the shield VS, the active zone V(x), the built-in potential of the junction Vbi, the material's permittivity εs, and the doping density ND. Since the active zone is low to moderately doped and the shield S is heavily doped, the depletion layer thickness can be approximated by the formula of a one-sided abrupt p+-n junction:
      W    ⁡          (      x      )        =                    2        ⁢                              ɛ            S                    ⁡                      [                                          V                ⁡                                  (                  x                  )                                            +                              V                S                            +                              V                bi                                      ]                                      qN        D            
Taking the junction-field-effect into account, non-linearity in fields up to 2T can be as high as 2%.